Question

Find the measure of the numbered angles in rhombus ABCD

Answer 1

see the explanation

Explanation:

we know that

In a Rhombus opposite angles are congruent and consecutive angles are supplementary

The diagonals are perpendicular and bisect the angles

so

step 1

Find the measure of angle 4

we know that

`m\angle 4=27^o` --->by the diagonals bisect the angles

step 2

Find the measure of angle 1

we know that

`m\angle 1=27^o` ----> by opposite angles are congruent

step 3

Find the measure of angle 2

we know that

`m\angle 1=m\angle 2` ----> by the diagonals bisect the angles

so

`m\angle 2=27^o`

step 4

Find the measure of angle 3

we know that

`m\angle 3=90^o` ----> by the diagonals are perpendicular

step 5

Find the measure of angle 5

we know that

`m\angle 5+27^o=90^o` ----> by complementary angles

`m\angle 5=90^o-27^o=63^o`

step 6

Find the measure of angle 6

we know that

`m\angle 6=m\angle 5` ----> by the diagonals bisect the angles

`m\angle 6=63^o`